Hybrid torque and SQUID magnetometry of individual magnetic nanotubes

For the experiments presented in this thesis, a hybrid magnetometer consisting of a ultra sensitive Si cantilever and a nano-scale superconducting quantum interference device (nanoSQUID) sensitive enough to measure a single nanoscale magnetic particle has been developed. The setup allows for two simultaneous and complementary measurements on individual nanoscale magnets. With dynamic cantilever magnetometry (DCM) a magnetic particle's magnetization integrated over its whole volume is determined. The nanoSQUID conversely is sensitive to the stray field emerging from the magnetic particle's lower end close to the nanoSQUID. This combination allows for extensive insight in the magnetic behaviour of individual
magnetic particles. DCM is a highly sensitive technique to measure the magnetization and anisotropy of small magnetic particles. The technique relies on the torque arising between an applied magnetic field and the magnetic moment of the particle under investigation, attached to the cantilever's tip. The torque leads to a virtual change of the cantilever's spring constant, effectively stiffening
or softening the cantilever, depending on the applied field and the magnetization. This change of the spring constant then results in a measurable shift of the cantilever's resonant frequency that can be analyzed. SQUIDs in general are the devices with highest sensitivity to magnetic flux. nanoSQUIDs in particular are additionally optimized to the detection of small magnetic particles by matching their loop size to the size of the detected particles. Magnetic field lines emerging from a particle's magnetization, that enclose the SQUID loop, lead to a voltage change across the device. The nanoSQUID is most sensitive to areas of the investigated elongated particle that are closest to it. Among nanoscale magnetic particles, nanotubes (NT) are a particularly interesting example. Due to their geometry they support magnetic configurations not present in bulk or other nanoparticle geometries. They avoid point singularities of magnetization that occur in solid cylinders and thus their magnetization is proposed to reverse fast and reproducibly. Furthermore, theoretical
analysis predicts a global vortex state. In this flux closure state, the NT's stray field is minimized that would allow for densely packing them without magnetic interference with neighbouring NTs. In the course of this thesis three different kinds of NTs with Ni, CoFeB and permalloy shells were investigated. The magnetic films of the NTs are all isotropic and thus exhibit only shape anisotropy. We use piezo-electric scanners that allow for free positioning of the nanoSQUID located below the cantilever hanging in pendulum-geometry to precisely map out the nanoSQUID's coupling characteristics in the three dimensional half space above the nanoSQUID. We then take
advantage of this information to optimally position the NT relative to the nanoSQUID in order to maximize the signal-to-noise ratio and consequently the sensitivity. The torque magnetometry data is evaluated using an analytical model for ellipsoidal magnetic particles on the basis of the Stoner-Wohlfarth model. The magnetization is assumed to be constant throughout the magnet and magnetic moments to reverse in unison. Based on these assumptions the energy of the magnet-on-cantilever system can be minimized to obtain an expression for the cantilever frequency shift, which ultimately depends on the magnetic energy's curvature. With this model, in the limit of high applied fields, the saturation magnetization of the three investigated NT samples can be extracted. In the limit of low applied fields, the frequency shift can be converted to the magnet-on-cantilever's magnetization. This allows to obtain hysteresis data of the volume magnetization which can then directly be compared to the stray flux measured by the nanoSQUID. Exploiting the setup's duality to obtain volume magnetization and stray flux and comparing this to micromagnetic simulations provides a powerful toolbox for analysis of magnetic properties. In the experiments on Ni NT we come to the conclusion that the film morphology and especially the distinct surface roughness has a significant influence on magnetization reversal. Comparing our data with micromagnetic simulations suggests the formation of vortex-like tubular domains in different segments of the NT instead of domains nucleating solely at the NT's ends.
On the other hand, comparing volume magnetization and stray flux in the case of the CoFeB NT, leads to the conclusion that the smooth CoFeB NT reverses by domain nucleation at the NT's end as theory predicts. Taking advantage of the temperature control in the cryostat, the exchange bias of a naturally oxidized permalloy NT is investigated. We explore the training effect and the temperature dependence of the NT's magnetization. We find a blocking temperature around 18 K suggesting the presence of a thin oxide layer with thickness < 5 nm. The composition of the permalloy's oxide layer is analyzed with x-ray absorption spectroscopy and we find evidence for the possible presence of different Ni and Fe oxides. Additionally, comparison of volume magnetization and stray flux provides insight in exchange bias influencing the NT's magnetization reversal. However, at elevated temperatures, where exchange bias is suppressed, reversal as expected from theoretical predictions can be verified with our hybrid magnetometer.